Question

The lines y=0.5x + 8 and y = 5-x are shown graphed to the right. Which of the following is the solution to the system comprised of these two lines?1) (0,5)2) (-2,7)3) (2,3)4) (4,10)

Answer 1

Graphically

As we can see in the graph, the lines intersect in the ordered pair (-2,7). Then, the solution to the system comprised of these two lines is:

`\begin{cases}x=-2 \\ y=7\end{cases}`

Mathematically

To solve the given system of equations, we can use the equalization method.

Step 1: Either variable is chosen and solved in both equations.

`\begin{cases}y=0.5x+8\Rightarrow\text{ Equation 1} \\ y=5-x\Rightarrow\text{ Equation 2}\end{cases}`

Step 2: The expressions are equalized, obtaining an equation with a variable.

`0.5x+8=5-x`

Step 3: We solve for x the resulting equation: